An innovative method, high-accuracy surface modelling (HASM), is presented, which is based on the fundamental theorem of surfaces. The fundamental theorem of surfaces makes sure that a surface is uniquely defined by the first and second fundamental coefficients. Numerical tests of a Gaussian synthetic surface show that the Root Mean Square Error of the HASM method is much less than the ones of classical methods, such as the Triangulated Irregular Network, Spline, Inverse Distance Weight and Kriging methods. The HASM method gives a solution to the error problem that has long troubled generations of digital elevation models. All the methods for surface modelling are used to simulate a Digital Elevation Map (DEM) of Qian-Yan-Zhou Experimental Station for Red Soil and Hilly Land, which has a great topographical variety. Shaded relief maps of the simulated DEMs are developed to represent the terrain relief of Qian-Yan-Zhou Experimental Station, which shows that simulation results of the HASM method are much better than the ones of classical methods.

We developed a method for high-accuracy surface modeling (HASM) in terms of the fundamental theorem of surfaces, which has theoretically found a solution for error problems. However, the computing speed of HASM was too slow to be widely applied in practice. Thus, adjustment computation of HASM (HASM-AC) is developed in this article. For comparatively testing HASM-AC accuracy, a mathematical surface is first selected so that the true value is able to be predetermined to avoid uncontrollable data errors. The numerical test indicates that HASM-AC has the highest accuracy and its accuracy is 20.67, 15.67, and 14.67 times higher than the inverse distance weighting (IDW), kriging, and spline, respectively. Then, a 0.4 km × 0.5 km rectangular area is used to test the effects of different spatial resolutions and sampling intervals on accuracy. This real-world test demonstrates that HASM-AC accuracy increases at a much better and stable pace as the spatial resolution becomes finer and sampling intervals get shorter, compared to the classic methods. Finally, the computing speed is tested in an area with 6000 × 6000 grid cells where Qinghai, Gansu, and Sichuan provinces meet. The computing speed of HASM-AC is 11, 8, and 563 times faster than IDW, spline, and kriging, respectively, which makes HASM-AC able to process data in a huge size and make real-time visualization realizable. In short, HASM-AC performs best in both the numerical and real-world tests.